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equation for kinetic energy of a spring. The total energy of the system of a block and a spring is equal to the sum of the potential energy stored in the spring plus the kinetic energy of the block and is proportional to the square of the amplitude ETotal 12kA2. E P m a x 1 2 k x m a x 2.
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Applying Equation 10 to the Lagrangian of this simple system we obtain the familiar differential equation for the mass-spring oscillator. But gravity will also do work on the ball Demo of Spring Launcher Work of Spring on ball ½ kx2 ½ mv2. It is a quantity that depends upon both mass and speed.
According to the previous expression the total energy is a constant of the motion and is proportional to the amplitude squared of the oscillation.
A quarter of the way through a cycle all that potential energy has gone to kinetic as the mass passes through. The usual formula for kinetic energy is ½mv2 which you have most likely seen before. 12mv2 12kx2 when the spring is stretched some distance x from the equilibrium point and when its mass also has some velocity v with which it is moving. E U K 1 2 k x 2 1 2 m v 2 We can find the mechanical energy E by evaluating the energy at one of the turning points.
